{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vehicle steering\n",
    "Karl J. Astrom and Richard M. Murray  \n",
    "23 Jul 2019\n",
    "\n",
    "This notebook contains the computations for the vehicle steering running example in *Feedback Systems*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMM comments to Karl, 27 Jun 2019\n",
    "* I'm using this notebook to walk through all of the vehicle steering examples and make sure that all of the parameters, conditions, and maximum steering angles are consitent and reasonable.\n",
    "* Please feel free to send me comments on the contents as well as the bulletted notes, in whatever form is most convenient.\n",
    "* Once we have sorted out all of the settings we want to use, I'll copy over the changes into the MATLAB files that we use for creating the figures in the book.\n",
    "* These notes will be removed from the notebook once we have finalized everything."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import control as ct\n",
    "ct.use_fbs_defaults()\n",
    "ct.use_numpy_matrix(False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vehicle steering dynamics (Example 3.11)\n",
    "\n",
    "The vehicle dynamics are given by a simple bicycle model.  We take the state of the system as $(x, y, \\theta)$ where $(x, y)$ is the position of the reference point of the vehicle in the plane and $\\theta$ is the angle of the vehicle with respect to horizontal.  The vehicle input is given by $(v, \\delta)$ where $v$ is the forward velocity of the vehicle and $\\delta$ is the angle of the steering wheel.  We take as parameters the wheelbase $b$ and the offset $a$ between the rear wheels and the reference point. The model includes saturation of the vehicle steering angle (`maxsteer`).\n",
    "\n",
    "* System state: `x`, `y`, `theta`\n",
    "* System input: `v`, `delta`  \n",
    "* System output: `x`, `y`  \n",
    "* System parameters: `wheelbase`, `refoffset`, `maxsteer` \n",
    "\n",
    "Assuming no slipping of the wheels, the motion of the vehicle is given by a rotation around a point O that depends on the steering angle $\\delta$.  To compute the angle $\\alpha$ of the velocity of the reference point with respect to the axis of the vehicle, we let the distance from the center of rotation O to the contact point of the rear wheel be $r_\\text{r}$ and it the follows from Figure 3.17 in FBS that $b = r_\\text{r} \\tan \\delta$ and $a = r_\\text{r} \\tan \\alpha$, which implies that $\\tan \\alpha = (a/b) \\tan \\delta$.\n",
    "\n",
    "Reasonable limits for the steering angle depend on the speed.  The physical limit is given in our model as 0.5 radians (about 30 degrees).  However, this limit is rarely possible when the car is driving since it would cause the tires to slide on the pavement.  We us a limit of 0.1 radians (about 6 degrees) at 10 m/s ($\\approx$ 35 kph) and 0.05 radians (about 3 degrees) at 30 m/s ($\\approx$ 110 kph).  Note that a steering angle of 0.05 rad  gives a cross acceleration of $(v^2/b) \\tan \\delta \\approx (100/3) 0.05 = 1.7$ $\\text{m/s}^2$ at 10 m/s and 15 $\\text{m/s}^2$ at 30 m/s ($\\approx$ 1.5 times the force of gravity)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vehicle_update(t, x, u, params):\n",
    "    # Get the parameters for the model\n",
    "    a = params.get('refoffset', 1.5)        # offset to vehicle reference point\n",
    "    b = params.get('wheelbase', 3.)         # vehicle wheelbase\n",
    "    maxsteer = params.get('maxsteer', 0.5)  # max steering angle (rad)\n",
    "\n",
    "    # Saturate the steering input\n",
    "    delta = np.clip(u[1], -maxsteer, maxsteer)\n",
    "    alpha = np.arctan2(a * np.tan(delta), b)\n",
    "\n",
    "    # Return the derivative of the state\n",
    "    return np.array([\n",
    "        u[0] * np.cos(x[2] + alpha),    # xdot = cos(theta + alpha) v\n",
    "        u[0] * np.sin(x[2] + alpha),    # ydot = sin(theta + alpha) v\n",
    "        (u[0] / b) * np.tan(delta)      # thdot = v/l tan(phi)\n",
    "    ])\n",
    "\n",
    "def vehicle_output(t, x, u, params):\n",
    "    return x[0:2]\n",
    "\n",
    "# Default vehicle parameters (including nominal velocity)\n",
    "vehicle_params={'refoffset': 1.5, 'wheelbase': 3, 'velocity': 15, \n",
    "                'maxsteer': 0.5}\n",
    "\n",
    "# Define the vehicle steering dynamics as an input/output system\n",
    "vehicle = ct.NonlinearIOSystem(\n",
    "    vehicle_update, vehicle_output, states=3, name='vehicle',\n",
    "    inputs=('v', 'delta'), outputs=('x', 'y'), params=vehicle_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vehicle driving on a curvy road (Figure 8.6a)\n",
    "\n",
    "To illustrate the dynamics of the system, we create an input that correspond to driving down a curvy road.  This trajectory will be used in future simulations as a reference trajectory for estimation and control."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMM notes, 27 Jun 2019:\n",
    "* The figure below appears in Chapter 8 (output feedback) as Example 8.3, but I've put it here in the notebook since it is a good way to demonstrate the dynamics of the vehicle.\n",
    "* In the book, this figure is created for the linear model and in a manner that I can't quite understand, since the linear model that is used is only for the lateral dynamics.  The original file is `OutputFeedback/figures/steering_obs.m`.\n",
    "* To create the figure here, I set the initial vehicle angle to be $\\theta(0) = 0.75$ rad and then used an input that gives a figure approximating Example 8.3  To create the lateral offset, I think subtracted the trajectory from the averaged straight line trajectory, shown as a dashed line in the $xy$ figure below.\n",
    "* I find the approach that we used in the MATLAB version to be confusing, but I also think the method of creating the lateral error here is a hart to follow.  We might instead consider choosing a trajectory that goes mainly vertically, with the 2D dynamics being the $x$, $\\theta$ dynamics instead of the $y$, $\\theta$ dynamics.\n",
    "\n",
    "KJA comments, 1 Jul 2019:\n",
    "\n",
    "0. I think we should point out that the reference point is typically the projection of the center of mass of the whole vehicle.\n",
    "\n",
    "1. The heading angle $\\theta$ must be marked in Figure 3.17b.\n",
    "\n",
    "2. I think it is useful to start with a curvy road that you have done here but then to specialized to a trajectory that is essentially horizontal, where $y$ is the deviation from the nominal horizontal $x$ axis. Assuming that $\\alpha$ and $\\theta$ are small we get the natural linearization of (3.26) $\\dot x = v$ and $\\dot y =v(\\alpha + \\theta)$\n",
    "\n",
    "RMM response, 16 Jul 2019:\n",
    "* I've changed the trajectory to be about the horizontal axis, but I am ploting things vertically for better figure layout.  This corresponds to what is done in Example 9.10 in the text, which I think looks OK.\n",
    "\n",
    "KJA response, 20 Jul 2019: Fig 8.6a is fine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 648x324 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# System parameters\n",
    "wheelbase = vehicle_params['wheelbase']\n",
    "v0 = vehicle_params['velocity']\n",
    "\n",
    "# Control inputs\n",
    "T_curvy = np.linspace(0, 7, 500)\n",
    "v_curvy = v0*np.ones(T_curvy.shape) \n",
    "delta_curvy = 0.1*np.sin(T_curvy)*np.cos(4*T_curvy) + 0.0025*np.sin(T_curvy*np.pi/7)\n",
    "u_curvy = [v_curvy, delta_curvy]\n",
    "X0_curvy = [0, 0.8, 0]\n",
    "\n",
    "# Simulate the system + estimator\n",
    "t_curvy, y_curvy, x_curvy = ct.input_output_response(\n",
    "    vehicle, T_curvy, u_curvy, X0_curvy, params=vehicle_params, return_x=True)\n",
    "\n",
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure(figsize=[9, 4.5])\n",
    "\n",
    "# Plot the resulting trajectory (and some road boundaries)\n",
    "plt.subplot(1, 4, 2)\n",
    "plt.plot(y_curvy[1], y_curvy[0])\n",
    "plt.plot(y_curvy[1] - 9/np.cos(x_curvy[2]), y_curvy[0], 'k-', linewidth=1)\n",
    "plt.plot(y_curvy[1] - 3/np.cos(x_curvy[2]), y_curvy[0], 'k--', linewidth=1)\n",
    "plt.plot(y_curvy[1] + 3/np.cos(x_curvy[2]), y_curvy[0], 'k-', linewidth=1)\n",
    "\n",
    "plt.xlabel('y [m]')\n",
    "plt.ylabel('x [m]');\n",
    "plt.axis('Equal')\n",
    "\n",
    "# Plot the lateral position\n",
    "plt.subplot(2, 2, 2)\n",
    "plt.plot(t_curvy, y_curvy[1])\n",
    "plt.ylabel('Lateral position $y$ [m]')\n",
    "\n",
    "# Plot the steering angle\n",
    "plt.subplot(2, 2, 4)\n",
    "plt.plot(t_curvy, delta_curvy)\n",
    "plt.ylabel('Steering angle $\\\\delta$ [rad]')\n",
    "plt.xlabel('Time t [sec]')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearization of lateral steering dynamics (Example 6.13)\n",
    "\n",
    "We are interested in the motion of the vehicle about a straight-line path ($\\theta = \\theta_0$) with constant velocity $v_0 \\neq 0$. To find the relevant equilibrium point, we first set $\\dot\\theta = 0$ and we see that we must have $\\delta = 0$, corresponding to the steering wheel being straight. The motion in the xy plane is by definition not at equilibrium and so we focus on lateral deviation of the vehicle from a straight line. For simplicity, we let $\\theta_\\text{e} = 0$, which corresponds to driving along the $x$ axis. We can then focus on the equations of motion in the $y$ and $\\theta$ directions with input $u = \\delta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linearized system dynamics:\n",
      "\n",
      "A = [[0. 1.]\n",
      " [0. 0.]]\n",
      "\n",
      "B = [[0.5]\n",
      " [1. ]]\n",
      "\n",
      "C = [[1. 0.]]\n",
      "\n",
      "D = [[0.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Define the lateral dynamics as a subset of the full vehicle steering dynamics\n",
    "lateral = ct.NonlinearIOSystem(\n",
    "    lambda t, x, u, params: vehicle_update(\n",
    "        t, [0., x[0], x[1]], [params.get('velocity', 1), u[0]], params)[1:],\n",
    "    lambda t, x, u, params: vehicle_output(\n",
    "        t, [0., x[0], x[1]], [params.get('velocity', 1), u[0]], params)[1:],\n",
    "    states=2, name='lateral', inputs=('phi'), outputs=('y')\n",
    ")\n",
    "\n",
    "# Compute the linearization at velocity v0 = 15 m/sec\n",
    "lateral_linearized = ct.linearize(lateral, [0, 0], [0], params=vehicle_params)\n",
    "\n",
    "# Normalize dynamics using state [x1/b, x2] and timescale v0 t / b\n",
    "b = vehicle_params['wheelbase']\n",
    "v0 = vehicle_params['velocity']\n",
    "lateral_transformed = ct.similarity_transform(\n",
    "    lateral_linearized, [[1/b, 0], [0, 1]], timescale=v0/b)\n",
    "\n",
    "# Set the output to be the normalized state x1/b\n",
    "lateral_normalized = lateral_transformed * (1/b)\n",
    "print(\"Linearized system dynamics:\\n\")\n",
    "print(lateral_normalized)\n",
    "\n",
    "# Save the system matrices for later use\n",
    "A = lateral_normalized.A\n",
    "B = lateral_normalized.B\n",
    "C = lateral_normalized.C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenvalue placement controller design (Example 7.4)\n",
    "\n",
    "We want to design a controller that stabilizes the dynamics of the vehicle and tracks a given reference value $r$ of the lateral position of the vehicle.  We use feedback to design the dynamics of the system to have the characteristic polynomial\n",
    "$p(s) = s^2 + 2 \\zeta_\\text{c} \\omega_\\text{c} + \\omega_\\text{c}^2$.\n",
    "\n",
    "To find reasonable values of $\\omega_\\text{c}$ we observe that the initial response of the steering angle to a unit step change in the steering command is $\\omega_\\text{c}^2 r$, where $r$ is the commanded lateral transition. Recall that the model is normalized so that the length unit is the wheelbase $b$ and the time unit is the time $b/v_0$ to travel one wheelbase. A typical car has a wheelbase of about 3 m and, assuming a speed of 30 m/s, a normalized time unit corresponds to 0.1 s. To determine a reasonable steering angle when making a gentle lane change, we assume that the turning radius is $R$ = 600 m. For a wheelbase of 3 m this corresponds to a steering angle $\\delta \\approx 3/600 = 0.005$ rad and a lateral acceleration of $v^2/R$ = 302/600 = 1.5 m/s$^2$. Assuming that a lane change corresponds to a translation of one wheelbase we find $\\omega_\\text{c} = \\sqrt{0.005}$ = 0.07 rad/s.\n",
    "\n",
    "The unit step responses for the closed loop system for different values of the design parameters are shown below. The effect of $\\omega_c$ is shown on the left, which shows that the response speed increases with increasing $\\omega_\\text{c}$. All responses have overshoot less than 5% (15 cm), as indicated by the dashed lines. The settling times range from 30 to 60 normalized time units, which corresponds to about 3–6 s, and are limited by the acceptable lateral acceleration of the vehicle. The effect of $\\zeta_\\text{c}$ is shown on the right. The response speed and the overshoot increase with decreasing damping. Using these plots, we conclude that a reasonable design choice is $\\omega_\\text{c} = 0.07$ and $\\zeta_\\text{c} = 0.7$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMM note, 27 Jun 2019: \n",
    "* The design guidelines are for $v_0$ = 30 m/s (highway speeds) but most of the examples below are done at lower speed (typically 10 m/s).  Also, the eigenvalue locations above are not the same ones that we use in the output feedback example below.  We should probably make things more consistent.\n",
    "\n",
    "KJA comment, 1 Jul 2019: \n",
    "* I am all for maikng it consist and choosing e.g. v0 = 30 m/s\n",
    "\n",
    "RMM comment, 17 Jul 2019:\n",
    "* I've updated the examples below to use v0 = 30 m/s for everything except the forward/reverse example.  This corresponds to ~105 kph (freeway speeds) and a reasonable bound for the steering angle to avoid slipping is 0.05 rad."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x324 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Utility function to place poles for the normalized vehicle steering system\n",
    "def normalized_place(wc, zc):\n",
    "    # Get the dynamics and input matrices, for later use\n",
    "    A, B = lateral_normalized.A, lateral_normalized.B\n",
    "    \n",
    "    # Compute the eigenvalues from the characteristic polynomial\n",
    "    eigs = np.roots([1, 2*zc*wc, wc**2])\n",
    "    \n",
    "    # Compute the feedback gain using eigenvalue placement\n",
    "    K = ct.place_varga(A, B, eigs)\n",
    "    \n",
    "    # Create a new system representing the closed loop response\n",
    "    clsys = ct.StateSpace(A - B @ K, B, lateral_normalized.C, 0)\n",
    "    \n",
    "    # Compute the feedforward gain based on the zero frequency gain of the closed loop\n",
    "    kf = np.real(1/clsys.evalfr(0))\n",
    "\n",
    "    # Scale the input by the feedforward gain\n",
    "    clsys *= kf\n",
    "    \n",
    "    # Return gains and closed loop system dynamics\n",
    "    return K, kf, clsys\n",
    "\n",
    "# Utility function to plot simulation results for normalized vehicle steering system\n",
    "def normalized_plot(t, y, u, inpfig, outfig):\n",
    "    plt.sca(outfig)\n",
    "    plt.plot(t, y)\n",
    "    plt.sca(inpfig)\n",
    "    plt.plot(t, u[0])\n",
    "    \n",
    "# Utility function to label plots of normalized vehicle steering system \n",
    "def normalized_label(inpfig, outfig):\n",
    "    plt.sca(inpfig)\n",
    "    plt.xlabel('Normalized time $v_0 t / b$')\n",
    "    plt.ylabel('Steering angle $\\delta$ [rad]')\n",
    "\n",
    "    plt.sca(outfig)\n",
    "    plt.ylabel('Lateral position $y/b$')\n",
    "    plt.plot([0, 20], [0.95, 0.95], 'k--')\n",
    "    plt.plot([0, 20], [1.05, 1.05], 'k--')\n",
    "\n",
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure(figsize=[9, 4.5])\n",
    "\n",
    "# Explore range of values for omega_c, with zeta_c = 0.7\n",
    "outfig = plt.subplot(2, 2, 1)\n",
    "inpfig = plt.subplot(2, 2, 3)\n",
    "zc = 0.7\n",
    "for wc in [0.5, 0.7, 1]:\n",
    "    # Place the poles of the system\n",
    "    K, kf, clsys = normalized_place(wc, zc)\n",
    "    \n",
    "    # Compute the step response\n",
    "    t, y, x = ct.step_response(clsys, np.linspace(0, 20, 100), return_x=True)\n",
    "        \n",
    "    # Compute the input used to generate the control response\n",
    "    u = -K @ x + kf * 1\n",
    "\n",
    "    # Plot the results\n",
    "    normalized_plot(t, y, u, inpfig, outfig)\n",
    "    \n",
    "# Add labels to the figure\n",
    "normalized_label(inpfig, outfig)\n",
    "plt.legend(('$\\omega_c = 0.5$', '$\\omega_c = 0.7$', '$\\omega_c = 0.1$'))\n",
    "\n",
    "# Explore range of values for zeta_c, with omega_c = 0.07\n",
    "outfig = plt.subplot(2, 2, 2)\n",
    "inpfig = plt.subplot(2, 2, 4)\n",
    "wc = 0.7\n",
    "for zc in [0.5, 0.7, 1]:\n",
    "    # Place the poles of the system\n",
    "    K, kf, clsys = normalized_place(wc, zc)\n",
    "    \n",
    "    # Compute the step response\n",
    "    t, y, x = ct.step_response(clsys, np.linspace(0, 20, 100), return_x=True)\n",
    "        \n",
    "    # Compute the input used to generate the control response\n",
    "    u = -K @ x + kf * 1\n",
    "\n",
    "    # Plot the results\n",
    "    normalized_plot(t, y, u, inpfig, outfig)\n",
    "    \n",
    "# Add labels to the figure\n",
    "normalized_label(inpfig, outfig)\n",
    "plt.legend(('$\\zeta_c = 0.5$', '$\\zeta_c = 0.7$', '$\\zeta_c = 1$'))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMM notes, 17 Jul 2019\n",
    "* These step responses are *very* slow.  Note that the steering wheel angles are about 10X less than a resonable bound (0.05 rad at 30 m/s).  A consequence of these low gains is that the tracking controller in Example 8.4 has to use a different set of gains.  We could update, but the gains listed here have a rationale that we would have to update as well.\n",
    "* Based on the discussion below, I think we should make $\\omega_\\text{c}$ range from 0.5 to 1 (10X faster).\n",
    "\n",
    "KJA response, 20 Jul 2019: Makes a lot of sense to make $\\omega_\\text{c}$ range from 0.5 to 1 (10X faster). The plots were still in the range 0.05 to 0.1 in the note you sent me.\n",
    "\n",
    "RMM response: 23 Jul 2019: Updated $\\omega_\\text{c}$ to 10X faster.  Note that this makes size of the inputs for the step response quite large, but that is in part because a unit step in the desired position produces an (instantaneous) error of $b = 3$ m $\\implies$ quite a large error.  A lateral error of 10 cm with $\\omega_c = 0.7$ would produce an (initial) input of 0.015 rad."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenvalue placement observer design (Example 8.3)\n",
    "\n",
    "We construct an estimator for the (normalized) lateral dynamics by assigning the eigenvalues of the estimator dynamics to desired value, specifified in terms of the second order characteristic equation for the estimator dynamics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L =  [[1.4]\n",
      " [1. ]]\n"
     ]
    }
   ],
   "source": [
    "# Find the eigenvalue from the characteristic polynomial\n",
    "wo = 1          # bandwidth for the observer\n",
    "zo = 0.7        # damping ratio for the observer\n",
    "eigs = np.roots([1, 2*zo*wo, wo**2])\n",
    "    \n",
    "# Compute the estimator gain using eigenvalue placement\n",
    "L = np.transpose(\n",
    "    ct.place(np.transpose(A), np.transpose(C), eigs))\n",
    "print(\"L = \", L)\n",
    "\n",
    "# Create a linear model of the lateral dynamics driving the estimator\n",
    "est = ct.StateSpace(A - L @ C, np.block([[B, L]]), np.eye(2), np.zeros((2,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear observer applied to nonlinear system output\n",
    "\n",
    "A simulation of the observer for a vehicle driving on a curvy road is shown below. The first figure shows the trajectory of the vehicle on the road, as viewed from above. The response of the observer is shown on the right, where time is normalized to the vehicle length. We see that the observer error settles in about 4 vehicle lengths."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMM note, 27 Jun 2019:\n",
    "* As an alternative, we can attempt to estimate the state of the full nonlinear system using a linear estimator.  This system does not necessarily converge to zero since there will be errors in the nominal dynamics of the system for the linear estimator.\n",
    "* The limits on the $x$ axis for the time plots are different to show the error over the entire trajectory.\n",
    "* We should decide whether we want to keep the figure above or the one below for the text.\n",
    "\n",
    "KJA comment, 1 Jul 2019:\n",
    "* I very much like your observation about the nonlinear system. I think it is a very good idea to use your new simulation\n",
    "\n",
    "RMM comment, 17 Jul 2019: plan to use this version in the text.\n",
    "\n",
    "KJA comment, 20 Jul 2019: I think this is a big improvement we show that an observer based on a linearized model works on a nonlinear simulation, If possible we could add a line telling why the linear model works and that this is standard procedure in control engineering.\t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x324 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert the curvy trajectory into normalized coordinates\n",
    "x_ref = x_curvy[0] / wheelbase\n",
    "y_ref = x_curvy[1] / wheelbase\n",
    "theta_ref = x_curvy[2]\n",
    "tau = v0 * T_curvy / b\n",
    "\n",
    "# Simulate the estimator, with a small initial error in y position\n",
    "t, y_est, x_est = ct.forced_response(est, tau, [delta_curvy, y_ref], [0.5, 0])\n",
    "\n",
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure(figsize=[9, 4.5])\n",
    "\n",
    "# Plot the actual and estimated states\n",
    "ax = plt.subplot(2, 2, 1)\n",
    "plt.plot(t, y_ref)\n",
    "plt.plot(t, x_est[0])\n",
    "ax.set(xlim=[0, 10])\n",
    "plt.legend(['actual', 'estimated'])\n",
    "plt.ylabel('Lateral position $y/b$')\n",
    "\n",
    "ax = plt.subplot(2, 2, 2)\n",
    "plt.plot(t, x_est[0] - y_ref)\n",
    "ax.set(xlim=[0, 10])\n",
    "plt.ylabel('Lateral error')\n",
    "\n",
    "ax = plt.subplot(2, 2, 3)\n",
    "plt.plot(t, theta_ref)\n",
    "plt.plot(t, x_est[1])\n",
    "ax.set(xlim=[0, 10])\n",
    "plt.xlabel('Normalized time $v_0 t / b$')\n",
    "plt.ylabel('Vehicle angle $\\\\theta$')\n",
    "\n",
    "ax = plt.subplot(2, 2, 4)\n",
    "plt.plot(t, x_est[1] - theta_ref)\n",
    "ax.set(xlim=[0, 10])\n",
    "plt.xlabel('Normalized time $v_0 t / b$')\n",
    "plt.ylabel('Angle error')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Output Feedback Controller (Example 8.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMM note, 27 Jun 2019\n",
    "* The feedback gains for the controller below are different that those computed in the eigenvalue placement example (from Ch 7), where an argument was given for the choice of the closed loop eigenvalues.  Should we choose a single, consistent set of gains in both places?\n",
    "* This plot does not quite match Example 8.4 because a different reference is being used for the laterial position.\n",
    "* The transient in $\\delta$ is quiet large.  This appears to be due to the error in $\\theta(0)$, which is initialized to zero intead of to `theta_curvy`.\n",
    "\n",
    "KJA comment, 1 Jul 2019:\n",
    "1. The large initial errors dominate the plots.\n",
    "\n",
    "2. There is somehing funny happening at the end of the simulation, may be due to the small curvature at the end of the path?\n",
    "\n",
    "RMM comment, 17 Jul 2019:\n",
    "* Updated to use the new trajectory\n",
    "* We will have the issue that the gains here are different than the gains that we used in Chapter 7.  I think that what we need to do is update the gains in Ch 7 (they are too sluggish, as noted above).\n",
    "* Note that unlike the original example in the book, the errors do not converge to zero.  This is because we are using pure state feedback (no feedforward) => the controller doesn't apply any input until there is an error.\n",
    "\n",
    "KJA comment, 20 Jul 2019: We may add that state feedback is a proportional controller which does not guarantee that the error goes to zero for example by changing the line \"The tracking error ...\" to \"The tracking error can be improved by adding integral action (Section7.4), later in this chapter \"Disturbance Modeling\" or feedforward (Section 8,5). Should we do an exercises? \t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K =  [[0.49   0.7448]]\n",
      "kf =  [[0.49]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x324 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the feedback gains\n",
    "# K, kf, clsys = normalized_place(1, 0.707)     # Gains from MATLAB\n",
    "# K, kf, clsys = normalized_place(0.07, 0.707)  # Original gains\n",
    "K, kf, clsys = normalized_place(0.7, 0.707)       # Final gains\n",
    "\n",
    "# Print out the gains\n",
    "print(\"K = \", K)\n",
    "print(\"kf = \", kf)\n",
    "\n",
    "# Construct an output-based controller for the system\n",
    "clsys = ct.StateSpace(\n",
    "    np.block([[A, -B@K], [L@C, A - B@K - L@C]]),\n",
    "    np.block([[B], [B]]) * kf, \n",
    "    np.block([[C, np.zeros(C.shape)], [np.zeros(C.shape), C]]), \n",
    "    np.zeros((2,1)))\n",
    "\n",
    "# Simulate the system\n",
    "t, y, x = ct.forced_response(clsys, tau, y_ref, [0.4, 0, 0.0, 0])\n",
    "\n",
    "# Calcaluate the input used to generate the control response\n",
    "u_sfb = kf * y_ref - K @ x[0:2]\n",
    "u_ofb = kf * y_ref - K @ x[2:4]\n",
    "\n",
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure(figsize=[9, 4.5])\n",
    "\n",
    "# Plot the actual and estimated states\n",
    "ax = plt.subplot(1, 2, 1)\n",
    "plt.plot(t, x[0])\n",
    "plt.plot(t, x[2])\n",
    "plt.plot(t, y_ref, 'k-.')\n",
    "ax.set(xlim=[0, 30])\n",
    "plt.legend(['state feedback', 'output feedback', 'reference'])\n",
    "plt.xlabel('Normalized time $v_0 t / b$')\n",
    "plt.ylabel('Lateral position $y/b$')\n",
    "\n",
    "ax = plt.subplot(2, 2, 2)\n",
    "plt.plot(t, x[1])\n",
    "plt.plot(t, x[3])\n",
    "plt.plot(t, theta_ref, 'k-.')\n",
    "ax.set(xlim=[0, 15])\n",
    "plt.ylabel('Vehicle angle $\\\\theta$')\n",
    "\n",
    "ax = plt.subplot(2, 2, 4)\n",
    "plt.plot(t, u_sfb[0])\n",
    "plt.plot(t, u_ofb[0])\n",
    "plt.plot(t, delta_curvy, 'k-.')\n",
    "ax.set(xlim=[0, 15])\n",
    "plt.xlabel('Normalized time $v_0 t / b$')\n",
    "plt.ylabel('Steering angle $\\\\delta$')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trajectory Generation (Example 8.8)\n",
    "\n",
    "To illustrate how we can use a two degree-of-freedom design to improve the performance of the system, consider the problem of steering a car to change lanes on a road.  We use the non-normalized form of the dynamics, which were derived in Example 3.11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "KJA comment, 1 Jul 2019:\n",
    "1. I think the reference trajectory is too much curved in the end compare with Example 3.11\n",
    "\n",
    "In summary I think it is OK to change the reference trajectories but we should make sure that the curvature is less than $\\rho=600 m$ not to have too high acceleratarion.\n",
    "\n",
    "RMM response, 16 Jul 2019:\n",
    "* Not sure if the comment about the trajectory being too curved is referring to this example.  The steering angles (and hence radius of curvature/acceleration) are quite low.  ??\n",
    "\n",
    "KJA response, 20 Jul 2019: You are right the curvature is not too small. We could add the sentence \"The small deviations can be eliminated by adding feedback.\"\n",
    "\n",
    "RMM response, 23 Jul 2019: I think the small deviation you are referring to is in the velocity trace.  This occurs because I gave a fixed endpoint in time and so the velocity had to be adjusted to hit that exact point at that time.  This doesn't show up in the book, so it won't be a problem ($\\implies$ no additional explanation required)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import control.flatsys as fs\n",
    "\n",
    "# Function to take states, inputs and return the flat flag\n",
    "def vehicle_flat_forward(x, u, params={}):\n",
    "    # Get the parameter values\n",
    "    b = params.get('wheelbase', 3.)\n",
    "    \n",
    "    # Create a list of arrays to store the flat output and its derivatives\n",
    "    zflag = [np.zeros(3), np.zeros(3)]\n",
    "    \n",
    "    # Flat output is the x, y position of the rear wheels\n",
    "    zflag[0][0] = x[0]\n",
    "    zflag[1][0] = x[1]\n",
    "    \n",
    "    # First derivatives of the flat output\n",
    "    zflag[0][1] = u[0] * np.cos(x[2])  # dx/dt\n",
    "    zflag[1][1] = u[0] * np.sin(x[2])  # dy/dt\n",
    "    \n",
    "    # First derivative of the angle\n",
    "    thdot = (u[0]/b) * np.tan(u[1])\n",
    "\n",
    "    # Second derivatives of the flat output (setting vdot = 0)\n",
    "    zflag[0][2] = -u[0] * thdot * np.sin(x[2])\n",
    "    zflag[1][2] =  u[0] * thdot * np.cos(x[2])\n",
    "    \n",
    "    return zflag\n",
    "\n",
    "# Function to take the flat flag and return states, inputs\n",
    "def vehicle_flat_reverse(zflag, params={}):\n",
    "    # Get the parameter values\n",
    "    b = params.get('wheelbase', 3.)  \n",
    "\n",
    "    # Create a vector to store the state and inputs\n",
    "    x = np.zeros(3)\n",
    "    u = np.zeros(2)\n",
    "    \n",
    "    # Given the flat variables, solve for the state\n",
    "    x[0] = zflag[0][0]  # x position\n",
    "    x[1] = zflag[1][0]  # y position\n",
    "    x[2] = np.arctan2(zflag[1][1], zflag[0][1])  # tan(theta) = ydot/xdot\n",
    "    \n",
    "    # And next solve for the inputs\n",
    "    u[0] = zflag[0][1] * np.cos(x[2]) + zflag[1][1] * np.sin(x[2])\n",
    "    thdot_v = zflag[1][2] * np.cos(x[2]) - zflag[0][2] * np.sin(x[2])\n",
    "    u[1] = np.arctan2(thdot_v, u[0]**2 / b)\n",
    "    \n",
    "    return x, u\n",
    "\n",
    "vehicle_flat = fs.FlatSystem(vehicle_flat_forward, vehicle_flat_reverse, inputs=2, states=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find a trajectory from an initial state $x_0$ to a final state $x_\\text{f}$ in time $T_\\text{f}$ we solve a point-to-point trajectory generation problem.  We also set the initial and final inputs, which sets the vehicle velocity $v$ and steering wheel angle $\\delta$ at the endpoints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x324 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the endpoints of the trajectory \n",
    "x0 = [0., 2., 0.]; u0 = [15, 0.]\n",
    "xf = [75, -2., 0.]; uf = [15, 0.]\n",
    "Tf = xf[0] / uf[0]\n",
    "\n",
    "# Define a set of basis functions to use for the trajectories\n",
    "poly = fs.PolyFamily(6)\n",
    "\n",
    "# Find a trajectory between the initial condition and the final condition\n",
    "traj = fs.point_to_point(vehicle_flat, x0, u0, xf, uf, Tf, basis=poly)\n",
    "\n",
    "# Create the trajectory\n",
    "t = np.linspace(0, Tf, 100)\n",
    "x, u = traj.eval(t)\n",
    "\n",
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure(figsize=[9, 4.5])\n",
    "\n",
    "# Plot the trajectory in xy coordinate\n",
    "plt.subplot(1, 4, 2)\n",
    "plt.plot(x[1], x[0])\n",
    "plt.xlabel('y [m]')\n",
    "plt.ylabel('x [m]')\n",
    "\n",
    "# Add lane lines and scale the axis\n",
    "plt.plot([-4, -4], [0, x[0, -1]], 'k-', linewidth=1)\n",
    "plt.plot([0, 0], [0, x[0, -1]], 'k--', linewidth=1)\n",
    "plt.plot([4, 4], [0, x[0, -1]], 'k-', linewidth=1)\n",
    "plt.axis([-10, 10, -5, x[0, -1] + 5])\n",
    "\n",
    "# Time traces of the state and input\n",
    "plt.subplot(2, 4, 3)\n",
    "plt.plot(t, x[1])\n",
    "plt.ylabel('y [m]')\n",
    "\n",
    "plt.subplot(2, 4, 4)\n",
    "plt.plot(t, x[2])\n",
    "plt.ylabel('theta [rad]')\n",
    "\n",
    "plt.subplot(2, 4, 7)\n",
    "plt.plot(t, u[0])\n",
    "plt.xlabel('Time t [sec]')\n",
    "plt.ylabel('v [m/s]')\n",
    "plt.axis([0, Tf, u0[0] - 1, uf[0] +1])\n",
    "\n",
    "plt.subplot(2, 4, 8)\n",
    "plt.plot(t, u[1]);\n",
    "plt.xlabel('Time t [sec]')\n",
    "plt.ylabel('$\\delta$ [rad]')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vehicle transfer functions for forward and reverse driving (Example 10.11)\n",
    "\n",
    "The vehicle steering model has different properties depending on whether we are driving forward or in reverse.  The figures below show step responses from steering angle to lateral translation for a the linearized model when driving forward (dashed) and reverse (solid). In this simulation we have added an extra pole with the time constant $T=0.1$ to approximately account for the dynamics in the steering system.\n",
    "\n",
    "With rear-wheel steering the center of mass first moves in the wrong direction and the overall response with rear-wheel steering is significantly delayed compared with that for front-wheel steering. (b) Frequency response for driving forward (dashed) and reverse (solid). Notice that the gain curves are identical, but the phase curve for driving in reverse has non-minimum phase."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMM note, 27 Jun 2019:\n",
    "* I cannot recreate the figures in Example 10.11.  Since we are looking at the lateral *velocity*, there is a differentiator in the output and this takes the step function and creates an offset at $t = 0$ (intead of a smooth curve).\n",
    "* The transfer functions are also different, and I don't quite understand why.  Need to spend a bit more time on this one.\n",
    "\n",
    "KJA comment, 1 Jul 2019: The reason why you cannot recreate figures i Example 10.11 is because the caption in figure is wrong, sorry my fault, the y-axis should be lateral position not lateral velocity. The approximate expression for the transfer functions\n",
    "\n",
    "$$\n",
    "G_{y\\delta}=\\frac{av_0s+v_0^2}{bs} = \\frac{1.5 s + 1}{3s^2}=\\frac{0.5s + 0.33}{s}\n",
    "$$\n",
    "\n",
    "are quite close to the values that you get numerically\n",
    "\n",
    "In this case I think it is useful to have v=1 m/s because we do not drive to fast backwards.\n",
    "\n",
    "RMM response, 17 Jul 2019\n",
    "* Updated figures below use the same parameters as the running example (the current text uses different parameters)\n",
    "* Following the material in the text, a pole is added at s = -1 to approximate the dynamics of the steering system.  This is not strictly needed, so we could decide to take it out (and update the text)\n",
    "\n",
    "KJA comment, 20 Jul 2019: I have been oscillating a bit about this example. Of course it does not make sense to drive in reverse in 30 m/s but it seems a bit silly to change parameters just in this case (if we do we have to motivate it). On the other hand what we are doing is essentially based on transfer functions and a RHP zero. My current view which has changed a few times is to keep the standard parameters. In any case we should eliminate the extra time constant. A small detail, I could not see the time response in the file you sent, do not resend it!, I will look at the final version.\n",
    "\n",
    "RMM comment, 23 Jul 2019: I think it is OK to have the speed be different and just talk about this in the text.  I have removed the extra time constant in the current version."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Forward TF =  \n",
      "          s + 1.333\n",
      "-----------------------------\n",
      "s^2 + 7.828e-16 s - 1.848e-16\n",
      "\n",
      "Reverse TF =  \n",
      "          -s + 1.333\n",
      "-----------------------------\n",
      "s^2 - 7.828e-16 s - 1.848e-16\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Magnitude of the steering input (half maximum)\n",
    "Msteer = vehicle_params['maxsteer'] / 2\n",
    "\n",
    "# Create a linearized model of the system going forward at 2 m/s\n",
    "forward_lateral = ct.linearize(lateral, [0, 0], [0], params={'velocity': 2})\n",
    "forward_tf = ct.ss2tf(forward_lateral)[0, 0]\n",
    "print(\"Forward TF = \", forward_tf)\n",
    "\n",
    "# Create a linearized model of the system going in reverise at 1 m/s\n",
    "reverse_lateral = ct.linearize(lateral, [0, 0], [0], params={'velocity': -2})\n",
    "reverse_tf = ct.ss2tf(reverse_lateral)[0, 0]\n",
    "print(\"Reverse TF = \", reverse_tf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure()\n",
    "\n",
    "# Forward motion\n",
    "t, y = ct.step_response(forward_tf * Msteer, np.linspace(0, 4, 500))\n",
    "plt.plot(t, y, 'b--')\n",
    "\n",
    "# Reverse motion\n",
    "t, y = ct.step_response(reverse_tf * Msteer, np.linspace(0, 4, 500))\n",
    "plt.plot(t, y, 'b-')\n",
    "\n",
    "# Add labels and reference lines\n",
    "plt.axis([0, 4, -0.5, 2.5])\n",
    "plt.legend(['forward', 'reverse'], loc='upper left')\n",
    "plt.xlabel('Time $t$ [s]')\n",
    "plt.ylabel('Lateral position [m]')\n",
    "plt.plot([0, 4], [0, 0], 'k-', linewidth=1)\n",
    "\n",
    "# Plot the Bode plots\n",
    "plt.figure()\n",
    "plt.subplot(1, 2, 2)\n",
    "ct.bode_plot(forward_tf[0, 0], np.logspace(-1, 1, 100), color='b', linestyle='--')\n",
    "ct.bode_plot(reverse_tf[0, 0], np.logspace(-1, 1, 100), color='b', linestyle='-')\n",
    "plt.legend(('forward', 'reverse'));\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feedforward Compensation (Example 12.6)\n",
    "\n",
    "For a lane transfer system we would like to have a nice response without overshoot, and we therefore consider the use of feedforward compensation to provide a reference trajectory for the closed loop system.  We choose the desired response as $F_\\text{m}(s) = a^22/(s + a)^2$, where the response speed or aggressiveness of the steering is governed by the parameter $a$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMM note, 27 Jun 2019:\n",
    "* $a$ was used in the original description of the dynamics as the reference offset.  Perhaps choose a different symbol here?\n",
    "* In current version of Ch 12, the $y$ axis is labeled in absolute units, but it should actually be in normalized units, I think.\n",
    "* The steering angle input for this example is quite high.  Compare to Example 8.8, above.  Also, we should probably make the size of the \"lane change\" from this example match whatever we use in Example 8.8\n",
    "\n",
    "KJA comments, 1 Jul 2019: Chosen parameters look good to me\n",
    "\n",
    "RMM response, 17 Jul 2019\n",
    "* I changed the time constant for the feedforward model to give something that is more reasonable in terms of turning angle at the speed of $v_0 = 30$ m/s.  Note that this takes about 30 body lengths to change lanes (= 9 seconds at 105 kph).\n",
    "* The time to change lanes is about 2X what it is using the differentially flat trajectory above.  This is mainly because the feedback controller applies a large pulse at the beginning of the trajectory (based on the input error), whereas the differentially flat trajectory spreads the turn over a longer interval.  Since are living the steering angle, we have to limit the size of the pulse => slow down the time constant for the reference model.\n",
    "\n",
    "KJA response, 20 Jul 2019: I think the time for lane change is too long, which may depend on the small steering angles used. The largest steering angle is about 0.03 rad, but we have admitted larger values in previous examples. I suggest that we change the design so that the largest sterring angel is closer to 0.05, see the remark from Bjorn O a lane change could take about 5 s at 30m/s. \n",
    "\n",
    "RMM response, 23 Jul 2019: I reset the time constant to 0.2, which gives something closer to what we had for trajectory generation.  It is still slower, but this is to be expected since it is a linear controller.  We now finish the trajectory in 20 body lengths, which is about 6 seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the desired response of the system\n",
    "a = 0.2\n",
    "P = ct.ss2tf(lateral_normalized)\n",
    "Fm = ct.TransferFunction([a**2], [1, 2*a, a**2])\n",
    "Fr = Fm / P\n",
    "\n",
    "# Compute the step response of the feedforward components\n",
    "t, y_ffwd = ct.step_response(Fm, np.linspace(0, 25, 100))\n",
    "t, delta_ffwd = ct.step_response(Fr, np.linspace(0, 25, 100))\n",
    "\n",
    "# Scale and shift to correspond to lane change (-2 to +2)\n",
    "y_ffwd = 0.5 - 1 * y_ffwd\n",
    "delta_ffwd *= 1\n",
    "\n",
    "# Overhead view\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(y_ffwd, t)\n",
    "plt.plot(-1*np.ones(t.shape), t, 'k-', linewidth=1)\n",
    "plt.plot(0*np.ones(t.shape), t, 'k--', linewidth=1)\n",
    "plt.plot(1*np.ones(t.shape), t, 'k-', linewidth=1)\n",
    "plt.axis([-5, 5, -2, 27])\n",
    "\n",
    "# Plot the response\n",
    "plt.subplot(2, 2, 2)\n",
    "plt.plot(t, y_ffwd)\n",
    "# plt.axis([0, 10, -5, 5])\n",
    "plt.ylabel('Normalized position y/b')\n",
    "\n",
    "plt.subplot(2, 2, 4)\n",
    "plt.plot(t, delta_ffwd)\n",
    "# plt.axis([0, 10, -1, 1])\n",
    "plt.ylabel('$\\\\delta$ [rad]')\n",
    "plt.xlabel('Normalized time $v_0 t / b$');\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fundamental Limits (Example 14.13)\n",
    "\n",
    "Consider a controller based on state feedback combined with an observer where we want a faster closed loop system and choose $\\omega_\\text{c} = 10$, $\\zeta_\\text{c} = 0.707$, $\\omega_\\text{o} = 20$, and $\\zeta_\\text{o} = 0.707$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "KJA comment, 20 Jul 2019: This is a really troublesome case. If we keep it as a vehicle steering problem we must have an order of magnitude lower valuer for $\\omega_c$ and $\\omega_o$ and then the zero will not be slow. My recommendation is to keep it as a general system with the transfer function. $P(s)=(s+1)/s^2$. The text then has to be reworded.\n",
    "\n",
    "RMM response, 23 Jul 2019: I think the way we have it is OK.  Our current value for the controller and observer is $\\omega_\\text{c} = 0.7$ and $\\omega_\\text{o} = 1$.  Here we way we want something faster and so we got to $\\omega_\\text{c} = 7$ (10X) and $\\omega_\\text{o} = 10$ (10X)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K =  [100.   -35.86]\n",
      "L =  [ 28.28 400.  ]\n",
      "C(s) =  \n",
      "-1.152e+04 s + 4e+04\n",
      "--------------------\n",
      "s^2 + 42.42 s + 6658\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the feedback gain using eigenvalue placement\n",
    "wc = 10\n",
    "zc = 0.707\n",
    "eigs = np.roots([1, 2*zc*wc, wc**2])\n",
    "K = ct.place(A, B, eigs)\n",
    "kr = np.real(1/clsys.evalfr(0))\n",
    "print(\"K = \", np.squeeze(K))\n",
    "\n",
    "# Compute the estimator gain using eigenvalue placement\n",
    "wo = 20\n",
    "zo = 0.707\n",
    "eigs = np.roots([1, 2*zo*wo, wo**2])\n",
    "L = np.transpose(\n",
    "    ct.place(np.transpose(A), np.transpose(C), eigs))\n",
    "print(\"L = \", np.squeeze(L))\n",
    "\n",
    "# Construct an output-based controller for the system\n",
    "C1 = ct.ss2tf(ct.StateSpace(A - B@K - L@C, L, K, 0))\n",
    "print(\"C(s) = \", C1)\n",
    "\n",
    "# Compute the loop transfer function and plot Nyquist, Bode\n",
    "L1 = P * C1\n",
    "plt.figure(); ct.nyquist_plot(L1, np.logspace(0.5, 3, 500))\n",
    "plt.figure(); ct.bode_plot(L1, np.logspace(-1, 3, 500));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K =  [100.   2.]\n",
      "C(s) =  \n",
      "    3628 s + 4e+04\n",
      "---------------------\n",
      "s^2 + 80.28 s + 156.6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Modified control law\n",
    "wc = 10\n",
    "zc = 2.6\n",
    "eigs = np.roots([1, 2*zc*wc, wc**2])\n",
    "K = ct.place(A, B, eigs)\n",
    "kr = np.real(1/clsys.evalfr(0))\n",
    "print(\"K = \", np.squeeze(K))\n",
    "\n",
    "# Construct an output-based controller for the system\n",
    "C2 = ct.ss2tf(ct.StateSpace(A - B@K - L@C, L, K, 0))\n",
    "print(\"C(s) = \", C2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the gang of four for the two designs\n",
    "ct.gangof4(P, C1, np.logspace(-1, 3, 100))\n",
    "ct.gangof4(P, C2, np.logspace(-1, 3, 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
